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Maharashtra SSC Class 10 Geometry March 2020 question paper

Maximum marks 40 · Time 2 hours

Try each question first, then open its model answer. Where the paper offers a choice, both questions are shown with OR between them.

Q.1 (A)

1 mark each

  1. Q.1 (A) (i)1 mark
    Out of the following which is the Pythagorean triplet?

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  2. Q.1 (A) (ii)1 mark
    Two circles of radii 5.55.5 cm and 3.33.3 cm respectively touch each other externally. What is the distance between their centres?

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  3. Q.1 (A) (iii)1 mark
    Distance of point (−3,4)(-3, 4) from the origin is ______.

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  4. Q.1 (A) (iv)1 mark
    Find the volume of a cube of side 33 cm:

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Q.1 (B)

1 mark each

  1. Q.1 (B) (i)1 mark
    The ratio of corresponding sides of similar triangles is 3:53 : 5, then find the ratio of their areas.
  2. Q.1 (B) (ii)1 mark
    Find the diagonal of a square whose side is 1010 cm.
  3. Q.1 (B) (iii)1 mark
    □ABCD\square ABCD is cyclic. If ∠B=110∘\angle B = 110^\circ, then find measure of ∠D\angle D.
  4. Q.1 (B) (iv)1 mark
    Find the slope of the line passing through the points A(2,3)A(2, 3) and B(4,7)B(4, 7).

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (i)2 marks
    OO is the centre of the circle, seg PS is a tangent segment and SS is the point of contact. Line PR is a secant. If PQ=3.6PQ = 3.6, QR=6.4QR = 6.4, find PS.
  2. Q.2 (A) (ii)2 marks
    If sec⁡θ=257\sec\theta = \dfrac{25}{7}, find the value of tan⁡θ\tan\theta.
  3. Q.2 (A) (iii)2 marks
    OO is the centre of the circle. Points AA, BB, XX, YY lie on the circle with XX on the minor side and YY on the major side of chord AB, and the central angle ∠AOB=100∘\angle AOB = 100^\circ (subtending arc AXB). Using the given information complete the following table:
    Type of arcName of the arcMeasure of the arc
    Minor arc
    Major arc

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (i)2 marks
    In △PQR\triangle PQR, NM∥RQNM \parallel RQ. If PM=15PM = 15, MQ=10MQ = 10, NR=8NR = 8, then find PN.
  2. Q.2 (B) (ii)2 marks
    In △MNP\triangle MNP, ∠MNP=90∘\angle MNP = 90^\circ, seg NQ⊥NQ \perp seg MPMP. If MQ=9MQ = 9, QP=4QP = 4, then find NQ.
  3. Q.2 (B) (iii)2 marks
    MM is the centre of the circle and seg KL is a tangent segment. LL is a point of contact. If MK=12MK = 12, KL=63KL = 6\sqrt{3}, then find the radius of the circle.
  4. Q.2 (B) (iv)2 marks
    Find the co-ordinates of midpoint of the segment joining the points (22,20)(22, 20) and (0,16)(0, 16).
  5. Q.2 (B) (v)2 marks
    A person is standing at a distance of 8080 metres from a Church and looking at its top. The angle of elevation is of 45∘45^\circ. Find the height of the Church.

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (i)3 marks
    In the given figure, XX is any point in the interior of the triangle DEF. Point XX is joined to the vertices of the triangle. seg PQ∥PQ \parallel seg DE, seg QR∥QR \parallel seg EF (with PP on XD, QQ on XE, RR on XF). Prove that seg PR∥PR \parallel seg DF.
  2. Q.3 (A) (ii)3 marks
    If A(6,1)A(6, 1), B(8,2)B(8, 2), C(9,4)C(9, 4) and D(7,3)D(7, 3) are the vertices of □ABCD\square ABCD, show that □ABCD\square ABCD is a parallelogram.

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (i)3 marks
    In △PQR\triangle PQR, point SS is the mid-point of side QR. If PQ=11PQ = 11, PR=17PR = 17, PS=13PS = 13, find QR.
  2. Q.3 (B) (ii)3 marks
    Prove that, tangent segments drawn from an external point to the circle are congruent.
  3. Q.3 (B) (iii)3 marks
    Draw a circle with radius 4.14.1 cm. Construct tangents to the circle from a point at a distance 7.37.3 cm from the centre.
  4. Q.3 (B) (iv)3 marks
    A metal cuboid of measures 1616 cm ×\times 1111 cm ×\times 1010 cm was melted to make coins. How many coins were made, if the thickness and diameter of each coin was 22 mm and 22 cm respectively? (π=3.14)(\pi = 3.14)

Q.4

4 marks each · attempt any 2

  1. Q.4 (i)4 marks
    In △ABC\triangle ABC, PQ is a line segment intersecting AB at P and AC at Q such that seg PQ∥PQ \parallel seg BC. If PQ divides △ABC\triangle ABC into two parts having equal areas, find BPAB\dfrac{BP}{AB}.
  2. Q.4 (ii)4 marks
    Draw a circle of radius 2.72.7 cm and draw a chord PQ of length 4.54.5 cm. Draw tangents at points PP and QQ without using centre.
  3. Q.4 (iii)4 marks
    □ABCD\square ABCD is a square of side 5050 m. Points PP, QQ, RR, SS are midpoints of side AB, side BC, side CD, side AD respectively. Find the area of the shaded region.

Q.5

3 marks each · attempt any 1

  1. Q.5 (i)3 marks
    Circles with centres AA, BB and CC touch each other externally. If AB=3AB = 3 cm, BC=3BC = 3 cm, CA=4CA = 4 cm, then find the radii of each circle.
  2. Q.5 (ii)3 marks
    If sin⁡θ+sin⁡2θ=1\sin\theta + \sin^2\theta = 1, show that: cos⁡2θ+cos⁡4θ=1\cos^2\theta + \cos^4\theta = 1.